In the English response to questions (p 46-47); Table
9 (p 45,titled “key outcome”) was mentioned 6 out of 8 table references. Table
9 for 300 wolves and 1 effective immigrant/six years retain more than 95 % of
the Gene Diversity for hundred years. Thus FRP=270 for Swedish wolf seems
sufficient to maintain diversity. Increase in inbreeding is in the long run
almost the same thing as loss in gene diversity, so if loss in diversity is
acceptable, so is increase in inbreeding. # Bruford´s summary (p 10) does not support FRP>270. A calculation
indicating FRP=370 is mentioned, but discarded after improved calculations
resulting in that FRP=270 is sufficient to keep decrease in diversity within 5
percent in hundred years. Inbreeding is raising is said to raise in hundred
years but not dramatically much.

# No clear support from Bruford for FRP>270 in responding SEPAs
questions. Five questions were asked which Bruford respond to (p 46-47). §1
Reasonable scenarios keep gene diversity and inbreeding in reasonable limits.
Effective migration is the key parameter, not numbers. §2 The SEPA proposal
FRP=417 given immigration 3.5 effective wolves per generation seem to overshoot
the needs for inbreeding and gene diversity. §3 insufficient information. §4 The
simulation suggests a loss of rare alleles. However, there are no citations to
guidelines what is acceptable and I do not think such exists. Allele loss is an
issue on higher levels of population hierarchy rather than regional Swedish. §5
Like question, 3 there is insufficient information.
Above the focus was that the most significant results seem to support that
FRP=270 is enough, while no results strongly contradict FRP=270. Below comments
are made weakening the value of results as support for FRP>270.

# Ten percent
retained ought to be enough for genetic viability. Bruford does not know
but asks for advice (p 55):“It would
be good to know if the retention of at least (or more than) 90% of the gene
diversity (Balmford et al. 1996, Frankham et al. 2013) or of at least (or more
than) 95% (Allendorf & Ryman 2002) in a subpopulation is a recommendation or
demand from conservation geneticists”, Two of three references suggest 10%,
the latest reference suggest 10%, all references which are not reviewers of
Brufords report suggest 10%. SEPA consider 10% when Bruford was mentioned in
its wolf management plan early 2015. When Bruford uses 5% it seems an
instruction and not his independent decision (p 63:“applying SEPA’s goal for
short-term conservation, i.e. retention of 95% of heterozygosity over 100 years”).
Ten percent probability of extinction is often regarded as a limit for demographic
viability, it seems extremely illogic the border for genetic diversity should
be smaller, extinction is certainly worse than a loss of a minor part of the
gene diversity.

# Reproducibility. The first demand is that a document should be
reproducible, thus the actual input in Vortex given to allow someone like me to
reproduce the results. This is not possible. E.g. *The allele frequencies of
the few loci used for the study are not given and a test with another set is not
shown (p34). The option used for capping is not given. The vital statistics
when the population is capped is not given. All the inputs in Vortex are not
well understood or given. Thus the simulations are not reproducible.

# Insufficient explanation, too hard or impossible to fully understand.
The text and explanations are not always understandable to me, besides that it
is hard to follow. In particular I do not understand how number of effective
immigrants can be exactly given. “Effective immigrant”/(year or generation)
should, as far as I understand, be a result of the simulation, not an input
(like for k). I do not understand how capping functions, thus what happens when
carrying capacity is reached. Can an immigrant vanish before it get progeny?
That would explain some of the “missing” immigrants. The structure of the
presentation is hard to understand. I note that some of the peer-rewiews seem
to base their evaluation on misunderunderstandings of the key results of the
information last added to the report, because premature information is still in
the report.

# Many input values irrelevant. The input viable statistic is not
relevant when the rules for removing wolves when “carrying capacity” is reached,
which is during most of the simulated time, different for different tested
alternatives. What I can see the values after carrying capacity is reached are
not mentioned or discussed.

# The Finnish and FennoScandia wolf populations are dealt with as no
immigration ever occurs. (p 34). The real word wolf “populations” are not
closed in that sense. There are more than ten thousand wolves in Europe except
Russia and twenty thousand in European Russia. Wolf move long distances, wolf genes
will pass through any geographic borders drawn in continental Europe. Wolve
genes outside FennoScandia will come to Finland and Scandinavia. The rate and
geographic distance of immigration is highly uncertain and future immigration
and population movements is still more uncertain. Any limit in the terrain
impassible by wolf genes will be arbitrary. But not to include that wolves can
move large distances is no solution to the problem.

# Neglected that effects of
high inbreeding and low diversity decays over time
At Ne at least 500 many scientists consider the negative effects of increase in
inbreeding and loss of gene diversity balanced by forces compensating for these
negative effects (adaptation, selection, decrease of the frequency of alleles
causing inbreeding depression, mutation, release of “hidden” genetic variation”
(e.g. in short term alleles on a chromosome segment are inherited together as a
single allele, but in long term this association is broken by crossing-over or
that a genetic block is circumvented by selection). In a FennoScandian
population with maybe a thousand wolves near the size when the effect of low
population size is compensated by other mechanisms, these forces will be
important and should be considered. This important effect reducing needed wolf
number and immigration are neglected. I guess the effect of decay of inbreeding
depression is faster and more important in a 10-20 generation perspective than
the decay of effect of low diversity
## The effect of high inbreeding decays
over time. Inbreeding using pedigree is not the essential, but inbreeding
depression. Formal inbreeding depend on how many generations back pedigree is
considered, the more generations back the pedigree is considered, the higher
will the relatedness of the parents be and thus the inbreeding of their progeny.
Inbreeding depression decreases by adaptation to the particular conditions. If
homozygosity of an allele is negative it will be selected against. Even many
alleles causing less drastic form of inbreeding depression are selected against,
but at a slower pace. Inbreeding itself responds, but only rather little to the
release of the genetic load (figure 6b). The coefficient of inbreeding maybe
what is shown in simulations, but inbreeding depression raises slower and may
sink even when inbreeding raises, and that is what matter. One may express it
that inbreeding caused by relatedness long back in the pedigree has less
effects than late relatedness. The study shows that decrease in inbreeding
depression by release of the genetic load is likely to be important (figure 5, figure
6a). p:19 “As expected, when the percentage load due to lethal equivalents was
high, the population recovered more rapidly due to the effects of purging
(removal of genetic load due to the death of homozygous individuals)”. The
wolves increase their vitality measured as population growth (in absence of the
“carrying capacity” limit) by near to a factor two, thus inbreeding depression
will be reduced to near half, thus equivalent to reducing “the effective
inbreeding” to somewhat more than half of the inbreeding figures mentioned. It has
been argued that dog breeders usually do not recommend matings resulting in
higher inbreeding than F=0.0625 (first cousin mating), but dog breeders usually
do not consider inbreeding by relatedness which tracks more than five
generations back. If Scandinavian wolves were treated as a race of dogs (as
wolves actually are), the inbreeding considered would now start to sink down to
say F=0.05, as old relatedness would be neglected. I do not suggest such a
drastic effect but my point is that it is recognized that relatedness of mates
is less important if the relatedness is many generation old.
## The effect of low diversity decays
over time. Vortex has a function for considering that the effects of low
diversity decays by mutations creating new genetic variation. But this was
neither used nor the effect discussed. As the populations discussed are not
very small compared to those which can be considered sustainable forever, it
must be considered in some way.

# Neglected that migrants get large offspring. That migrants
offspring is not inbred and wherefore contribute more than other parents is
neglected. This is acknowledged by the author (p10: “it is predicated on the
assumption that immigrants have similar reproductive success to residents
(there is circumstantial evidence that immigrant can outperform residents)). I
have guessed the effects of migration is 25% higher than results indicate for
that reason. But some effect of inbreeding on reproduction may be considered
# Improper way of culling when “carrying
capacity” is reached. Hunting doubles the impact of immigrants! Circumstances
change drastically when a population grows up to the artificial ceiling input
into Vortex (the population growth is constrained to the “carrying capacity” as
the author calls it with a misleading terminology). No information seems to be
given about the population control which keeps population at carrying capacity
“by environment” (p14: “total number of individuals that the environment can
allow”). The “environment” capping Scandinavian wolf to a non-growing
population is hunting. It is not understandable to me that the mortality of
wolf in the input is independent of if 15% of the population is shot or not, as
the author seems to suggest (Table 3 p 19). The key is that immigrants and
their progeny are intentionally more seldom shot than other wolves (that is
easy as immigrants and their offspring keeps geographically known territories
where quota hunting is not done). This results in less inbreeding and more gene
diversity than if culling is done at random as I think it is when carrying
capacity is reached. Quantitatively it seemed reasonable to me that to protect
immigrants and their offspring from shooting results in a doubling of the
impact of immigration. I explained that e.g. Lindgren D
2011. Licensjakt minskar inaveln. Svensk jakt 2011(8): 34-35. When I estimated that shooting wolves according
to the rules, which have been applied till now in Sweden, doubles the effect of
immigration compared to the random culling. My estimation of the influence of
hunting and immigrant superiority at https://vargdag.wordpress.com/2012/07/23/inavel_om_ett_sekel/ The inbreeding values will be higher as I have
disregarded relatedness among immigrants, but still the relations of
alternatives are informative. I believe Vortex does consider this selection and
superiority of immigrants and their progeny when reaching the carrying
capacity. I have considered the practical difficulties involved and that the
wolf population was kept constant by shooting (culling), not growing as has
been practiced till now. Liberg O, and Sand H. 2012. Effects of migration and
selective harvest for the genetic status of the Scandinavian wolf population. A
report to the Swedish Environment Protection Agency SEPA (Naturvårdsverket).
Grimsö Wildlife research Station, Swedish University of Agricultural Sciences.
19 s. has made computations mainly in agreement with my predictions. These have
been tested in court which did not object to the calculations but thought the
intended application had too small effect (shooting a quarter of the population
growth a single year long after the last migration event does not give a big
effect if shooting all growth forever doubles the effect of migration). Olof
Liberg has told me he works on a scientific publication on that, I hope he
submits the draft to this investigation. I directly condemn the unwillingness
of Naturvårdsverket to take actions involve this effect of hunting in the
evaluation of FRP and see that it is not considered in the Bruford report.

# The low effect of high immigration is contra-intuitive We Swedes
have been trained that immigrants bring new blood to the wolf population. Of
course we understood that there is some relatedness both between immigrants and
between immigrants and the Scandinavian population, but Swedes have seen from reports
supported by genetic data and statements that two immigrants in two decades was
enough to keep inbreeding, gene diversity and number of alleles about constant.
I think it needs more than a report with doubtful results to change that view
or act as it was radically changed. The report makes a verifiable prediction
about loss of alleles since 2012. I would like to see the predicted decrease in
number of alleles some decades, rather than just trusting in the prediction.

# Only immigration from Finland assumed, not Finland/Karelia (p 34)
“I therefore chose to use the Finland population allele frequencies for the
second population” A reviewer was misled to believe that the Karelian
population was a possible immigrant source, P65: “the Finnish and Karelian
populations are genetically diverged (FST ~ 0.1) and can currently not be
considered to represent one panmictic population.” Also
evidently Naturvårdsverket has misunderstood what they asked for; p3: “de
invandrande vargarna då har

genetiska egenskaper likt de finsk-karelska.”I am sure many other
readers make the same mistake.
The first two immigrant males Y-chromosome haplotypes were special. These
haplotypes could not be found outside Scandinavia in a sample of 86 males where
15 other haplotypes were found (Sundqvist et al 2001). Finland had four of
these other haplotypes. That indicates that the origins of the males is
distant, probably beyond Finland. The first immigrant female haplotype (mtDNA)
Lu-3 of the first female immigrant was not found in Finland and the somatic
chromosome DNA was highly differentiated from the Finnish wolves. Thus it seems
that immigrating wolves often carry genes from larger distance than Finland
(may be in some generation steps so the fathers father or mothers mother originated
in Russia). Immigrants to Finland (refreshing the wolves of the assumed source
population) and Sweden from Russia (Russian Karelia) are not considered. This
means that the allele frequencies reflect a source population which is more
related to Scandinavia and to itself than is the case for the source. There
will be some other rare alleles in the source population and wherefore the drop
in alleles will be overestimated. The impact of immigration on heterozygosity,
inbreeding and rare alleles are somewhat underestimated.

# No information about allele frequencies or selection grounds of used
loci(P 64): “The allele
frequencies + dispersal model is said to use empirical estimates on allele
frequencies in Finland, Karelia, and Scandinavia. However, information is
missing on the frequencies that were used, the number of individuals from which
they were estimated, pairwise FST values between populations,
diversity indices at different loci, and information on from where in Finland
and Karelia samples originated (as we have pointed out in previous reviews).”
No information about how the loci utilized were chosen, where may be a bias in
selection, it is impossible to evaluate as the information is not given.

# Statistical sampling error of loci neglected. (p 34): “Allele
frequencies for the first five markers were selected” (p 34): “although
parallel simulations using the second five markers were carried out as a
control for a small number of scenarios and the results were similar (data not
shown).” The effect of immigration on heterozygosity and allele occurrence is
highly depending on the allele frequencies of the recipient and donor
population in the actual specific locus. As I understand it: if common alleles
are more common and rare allele less common in the source than the recipient
population, the effect of immigration will be less heterozygosity and fewer
alleles!! This contra-intuitive response can happen for an individual locus
because of statistical variation, but not on average for a sufficient large
sample of loci. If the loci used behave in this odd way cannot be seen without
inspection, and I have no idea if five is a generally sufficient sample size. That
the author claims that similar results are obtained with a small number of - not
shown - simulated scenarios with five other loci increases the probability that
results are not severely affected by statistical sampling error. But the
unwillingness of the author to neither discuss the possible magnitude of the
statistical error; or show the results of validation runs done; or show the
allele frequencies of the actual loci - weakens the trust in the surprising
results of the low migration impact. I suggest ascribing part of this observed
low migration impact to this statistical error rather than reflecting real
relatedness.

# Vortex fails and the application of the report is thus generally not
very trustworthy. According to the author Vortex fails in two of three
models (predict the past and PS). Many think the third model (allele and
dispersal) applied suggests too small effect of immigration. Thus, the rapport
application of Vortex simulations generally is not very trustworthy and results
should not be regarded as safe.
## The more understandable and
established simulation of two simulation models was disregarded partly because
of the odd results. The simpler, more established and more transparent
model till now used as main model (PS), was discarded arguing its results
seemed unreasonable. In the Swedish summary (p 9): ”PS-modellen visade även
orealistiskt låg populationstillväxt; (p 30) “The mean final population size
was 550 ± 237 (carrying capacity 700)”; …(p 60): “this indicates the model has
a problem.”(p 39) “Of concern is the
observation that the predicted inbreeding coefficient using this model did not
vary as a function of population size for a given supplementation rate. These
two parameters are expected to covary under standard population genetic models,
suggesting that this model may not be responding in a predictable manner.” P 69:
a reviewer (and the author) “As the author points out, there is reason to be
concerned about the fact that when pedigree data were linked to Vortex,
predicted inbreeding coefficient was completely unaffected by population size…
This absence of covariation between population size and final inbreeding
coefficient seems to contradict all previous theory and modeling experience
within the field. Since there is no plausible biological explanation for this
result.” P 64: “inbreeding appears to increase independently of population size
under the pedigree +supplementation model… which is not expected under
traditional population genetics theory.” I make the same reflection myself,
population size ought to influence the speed inbreeding change as a result of
migration before equilibrium is close. I had expected to see more of that in
the figures showing the development of inbreeding over time, and equilibrium
should not be that close after 50 years for many wolves. That was actually an
important reason for me to believe in rather low wolf numbers to reduce
inbreeding at the next decades, but if the Tiveden wolves do not get progeny
that argument becomes weaker.
## The PS model does reduce inbreeding
as much as expected! The inbreeding expected after “a large number of
generations” is a function only of the number of immigrants per generation.
Each generation the equilibrium comes closer. From Figure 10 it seems evident
that the number of generations is enough to approach equilibrium. Shown in https://vargdag.wordpress.com/2012/11/12/framtida-inavel-funktion-av-migration/ The formula which is sufficient for good for
wolf is F=1/(4M+1) where M is immigrants per generation. I use the values from
Supplement Table 3 for the small population size (there the equilibrium should
occur faster). Immigrants assuming 5 years generation interval

Immigrants per generation

M

Inbreeding at equilibrium

F=1/(4M+1)

Vortex result after 50 years

Suppl Table 3

Start value around F=0.27

0.41=5*1/12

0,38

0.27

0.83=5*1/6

0,23

0.25

1.67=5*1/3

0,13

0.22

3.33=5*2/3

0,07

0.18

The deviation from
expected are huge and puzzling. Low immigration leads to considerable lower
inbreeding than expected and a high migration to a much higher level of
inbreeding than expected. I cannot see an acceptable explanation. This large
deviations from the “Island model” has also focused attention of reviewers P59:
“why these values deviate so much from the values expected from the so called Island
model. For example, the model result for 4 migrants/3 years is F =0.147. The
theoretical equilibrium value for this scenario is F = 0.036 with a generation
time of 5 years, and F = 0.045 with generation time of 4 years.” That the
response of the PS model seems weird does not give trust in that weird results
with other models are more trustworthy.## Vortex
predicts that the Swedish wolf would have gone extinct but it did not!The author tries to apply Vortex to the past
history of the Scandinavian wolf, with the result that Vortex simulations
predicts it would have gone extinct (p 16 ): “The implication of this result,
given the parameters used here, is that the persistence of the Swedish wolf
population was a statistically unlikely event” … “even under the least severe
inbreeding model, the projected population size at 2008 was only 57% of the
actual value”. Thus Vortex cannot predict the past, how could it when be trusted
to predict the future? Possible explanations are that the genes of the founders
are resistant to inbreeding depression, or the hybrid vigor observed for
immigrants has not been fully considered. But no effort to use this information
in the real runs were done, leading to too low estimates of FRP.

# The statistical precision of differences among alternatives tend to be
low and thus many results statistically insignificant. Look at standard
deviations of the results when presented in Tables and figures! Remember that a
95% confidence interval is double as large!

# The predictions of the fate of a real single wolf population is highly
uncertain.Example look at Figure
12a (or any of the figures for no immigration and variation shown). Remark: an
individual population may come considerable longer from the mean than a
standard deviation. It looks like good chance that the “inbreeding” of “the
Scandinavian wolf” will sink during the following fifty years even if there is
no immigration at all.

# Too detailed control over the report by Naturvårdsverket. The study
is governed in detail by instructions from SEPA, which seems too narrow, shadow
some relevant and highlight some less relevant considerations. Too little room
for own initiatives seems left to this qualified expert. The instructions seem
partly governed by irrelevant motives.

# Where is much positive to say about the report and positive critics,
which I do not spend much space, effort and time to express here. The allele
and dispersal method offer many potential advantages in theory and should be
possible to develop to more trustworthy application. The report give a better
understanding even if it does not reach to trustworthy practical application.
My critical remarks should not be interpreted as against the competence,
abilities, cooperation or scientific ambition of Prof Bruford. I do not think
the task could have been better done by anyone else given the rather narrow
task specified by SEPA and the limited budget and time frame. But it was not
enough to make a trustworthy sufficiently good foundation to give sufficient
accurate replies to the questions or to support a possible increase of FRP.

# My scientifically founded opinion: I claim as professor of genetics
that it is beyond reasonable doubt that increasing FRP now will have a very
small effect on the probability that wolf remains in Sweden in a sustainable
condition 2115.

# I am personally frustrated that a qualified analyses using Vortex
did not produce more trustworthy results, I predicted it should perform better
than it did, and regard the shortcoming of the report as a personal
shortcoming.

# Wolf management is more about psychology than Science. Probably it
does not help psychologically to base so called scientific decisions on a
report by a foreign expert which is so difficult to understand, comprehend and
accept as the Bruford report. It helps if wolf can come off the agenda, so
thinking how to do that can be a good idea. But the likelihood wolf leaves the
agenda is not helped by reports which opens more questions than they answer. It
helps with a material the most concerned parties can discuss about, but this
report will leave them out of the discussion.

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